During the design of a complete system, for example an aircraft, there may appear, for example by virtue of modifications of the specifications of the complete system, a requirement to modify geometrical characteristics of a known object, the geometric and mechanical characteristics of which are known.
Such dimensional modification of a known three-dimensional part notably involves calculations of mechanical resistance to certain dimensioning forces. These calculations, most often using finite element type numerical methods, involve modeling the part addressing the stated objectives of the calculations and modifications of shape. This modeling includes a so-called idealization phase, in which an operator proceeds to simplify the part to highlight the elements of its structure, notably its stiffeners, thin walls, etc., that can be modeled by plates, shells, etc. and thereby address the corresponding calculation objectives. Idealization therefore refers to geometrical transformations in which a subset of a volume may be transformed into a surface or a line respectively representative of a plate or a shell or indeed a beam in the case where the geometrical element is a line. This idealization phase produces a so-called idealized model of the initial object. This idealized model could be processed using a finite element type approach. The results of these calculations could lead to modifications to the dimensions of the initial object in order to respond to the modifications of the specification.
At present, the idealization transformations are essentially done manually. Access to parameterization and to decomposition of an object suited to the requirement of a discipline is, at best, linked to the construction tree of that object, as it exists in the CAD (computer-assisted design) environment or more generally in geometrical modeling software capable of associating a construction tree with the geometrical model of an object.
Very often there is no simple way to satisfy the shape modification requirements because:                the construction tree is lost if the geometrical model of the object has to be transferred between the software in which it was created and some other software meeting the requirement of some other discipline,        the 3D object is described only by a single construction tree generated by the user during the construction of the object.        
There are employed in the remainder of the description numerous terms borrowed from mathematical graph theory, from topology: graph, tree, CW complex, etc. These terms are employed with their standard meaning in that theory.
In CAD, a construction tree is defined as an ordered sequence of shape generation processes (also referred to as generative processes corresponding to the creation of primitives) usually created by a CAD modeler when designing an object by so-called B-Rep (Boundary Representation: surface modeling of a volume by its boundary: faces, edges and vertices).
However, in numerous configurations such a construction tree does not provide all the required properties: modifications of dimensions, idealization process for finite element analysis, etc. This remark naturally applies in all cases where the 3D object is not associated with a construction tree, which is a frequent situation in the case of designing complete systems.
The best known CAD (computer-assisted design) and simulation software offer idealization functions that are not highly automated and not very robust. They also offer decomposition into shape features and into primitives (basic cylinder, cone, cube, etc. shapes) that are limited to a single construction tree and are not very well suited to idealization because the primitives that they contain are often not suitable for idealization processes. Moreover, CAD software associates objects with trees that are necessarily binary, i.e. a single primitive is added to the shape of the intermediate object in each construction step, i.e. at each node of the construction tree.